Many MPs have expressed concerns about the backstop, aimed at preventing a “hard border” between Northern Ireland and the Republic of Ireland, which will remain in the EU, if no trade deal is ready before the end of the post-Brexit transition period.

It would mean Northern Ireland staying aligned to some EU rules, which many MPs say is unacceptable. The UK would also not be able to leave the backstop without EU agreement.

Downing Street has dismissed reports the vote could be delayed, although the chairman of Tory backbenchers, Sir Graham Brady has said he would “welcome the vote being deferred” if it meant concerns about the backstop could be addressed.

But Health Secretary Matt Hancock, who is among cabinet ministers promoting the deal in a series of visits on Friday, told BBC Radio 4’s Today programme that “the best thing for the country” was for MPs to back Mrs May’s deal: “I think we should win the vote, don’t pre-judge it.”

“My view is we should continue the debate. We’ve had three days, there’s two days more. I think we should make the argument, make the case and persuade people – that’s what you have Parliamentary debate for.”

Media captionJo Johnson and Stephen Kinnock argue for and against an alternative Brexit option

And Brexit Secretary Stephen Barclay, on a visit to an engineering firm in Peterborough, argued that businesses want the “certainty” of a Brexit deal and urged MPs to back it, as “a way of honouring the referendum result”.

The prime minister has suggested that MPs could be “given a role” in deciding whether to activate the backstop, and on Thursday night, a Tory backbench amendment was laid down intended to do that.

The amendment – which is understood to have government support – would also give the devolved administrations, particularly the Northern Ireland Assembly, although it is currently suspended, more say in the process.

It would also press the UK and EU to agree a future trade deal within a year of the implementation period ending.

Former Northern Ireland minister Hugo Swire tabled the amendment along with Bob Neill and Richard Graham.

Mr Swire told the BBC the amendment offered something that was “better than the current situation”.

Many Tory MPs would like to see the backstop “disappear altogether or be time limited”, he said, but the European Commission had said they would not re-open negotiations on the withdrawal agreement, so the amendment was “about the nearest we feel we can probe”. He said it was aimed at “people like me, who would like to be able to support this deal but find they are unable to”.